Eric Olhats, who stopped working with Griezmann over three years ago, accused Messi of running a "regime of terror" at Barcelona two weeks ago. A few days later, Griezmann's uncle said it's "not easy" playing for the same club as Messi.
Those remarks prompted Messi to say he's "tired of being the root of every problem at this club" and catapulted his relationship with Griezmann into the spotlight.
"It's time to put things in their place because I have been putting up with comments for a long while and now it's time to say enough," Griezmann said in an interview with Movistar on Monday.
"I've not had a relationship with Eric since I got married. He was invited to the wedding, but he didn't come. I got angry and I have not seen him since.
"My agent is my sister, but she doesn't speak. Neither do my parents. So as no one speaks, [Eric] answers the call and offers an opinion, as anyone can. That can do a lot of damage, it can create doubts in the dressing room and about my relationship with Leo.
"Leo knows I have a lot of respect and admiration for him. I learn from him. But it hurts a lot.
"And then my uncle, he doesn't know how football works. A journalist comes and wants a phrase out of you. You chat for an hour and you're careful about what you say, then they seem like your friend but, in the end, they just want to get a headline out of you.
"I told Leo I have nothing to do with them. I don't speak to them. I haven't spoken with Eric in three years and I don't even have my uncle on WhatsApp."
Griezmann, 29, joined Barca from Atletico Madrid in 2019 for €120 million and lamented that his time at Camp Nou has been filled with criticism and negative stories.
His signing 18 months ago came a year after he had turned down the chance to move to Barca in a documentary called The Decision -- an imitation of LeBron James' 2010 announcement that he would be signing with the Miami Heat.
Griezmann's decision came after Messi had publicly backed his signing and the France forward explained his now teammate was annoyed by his rejection.
"I spoke with Leo after I arrived and he told me that when I rejected the chance to come the first time, it annoyed him, because he had made public comments," Griezmann said.
"But since I have been part of the team, been teammates with him, he's always said he's with me until the end and I notice that and feel that every day."
Griezmann, who added that having to play under three coaches since joining Barca has made it difficult to settle in, said he hoped his decision to speak out will keep people off his back.
"Barcelona backed me by bringing me here and I want to return that confidence by helping the team win," he said. "There's no problem with anyone, I just ask that I am left in peace!"